Comptes Rendus
The effect of perturbations on the first eigenvalue of the 𝐩-Laplacian
Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 255-258.

Let Ω be a domain with Lipschitzian boundary of a compact Riemannian manifold (M,g) and p>1. We prove that we can make the volume of M arbitrarily close to the volume of (Ω,g) while the first eigenvalue of the p-Laplacian on M remains uniformly bounded from below in terms of the the first eigenvalue of the Neumann problem for the p-Laplacian on (Ω,g).

Soit Ω un domaine à bord Lipschitz d'une variété riemannienne compacte (M,g) et p>1. Nous montrons qu'on peut rendre le volume de M arbitrairement proche du volume de (Ω,g) tout en gardant la première valeur propre du p-Laplacien sur M uniformement minorée en termes de la première valeur propre du problème de Neumann pour le p-Laplacien sur (Ω,g).

Received:
Accepted:
Published online:
DOI: 10.1016/S1631-073X(02)02464-0

Ana-Maria Matei 1

1 McMaster University, Department of Mathematics and Statistics, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada
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Ana-Maria Matei. The effect of perturbations on the first eigenvalue of the $ \mathbf{p}$-Laplacian. Comptes Rendus. Mathématique, Volume 335 (2002) no. 3, pp. 255-258. doi : 10.1016/S1631-073X(02)02464-0. https://comptes-rendus.academie-sciences.fr/mathematique/articles/10.1016/S1631-073X(02)02464-0/

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